The Geometry And Topology Of Coxeter Groups Lms 32

Author : Michael Davis
Publisher : Princeton University Press
Page : 600 pages
File Size : 54,6 Mb
Release : 2012-11-26
Category : Mathematics
ISBN : 9781400845941

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The Geometry and Topology of Coxeter Groups. (LMS-32) by Michael Davis Pdf

The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.

Author : Peter J. Forrester
Publisher : Princeton University Press
Page : 808 pages
File Size : 50,8 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781400835416

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Log-Gases and Random Matrices (LMS-34) by Peter J. Forrester Pdf

Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painlevé transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory. This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field.

Author : Anne Thomas
Publisher : Unknown
Page : 128 pages
File Size : 40,9 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 3037196890

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Geometric and Topological Aspects of Coxeter Groups and Buildings by Anne Thomas Pdf

Coxeter groups are groups generated by reflections, and they appear throughout mathematics. Tits developed the general theory of Coxeter groups in order to develop the theory of buildings. Buildings have interrelated algebraic, combinatorial and geometric structures, and are powerful tools for understanding the groups which act on them. These notes focus on the geometry and topology of Coxeter groups and buildings, especially nonspherical cases. The emphasis is on geometric intuition, and there are many examples and illustrations. Part I describes Coxeter groups and their geometric realisations, particularly the Davis complex, and Part II gives a concise introduction to buildings. This book will be suitable for mathematics graduate students and researchers in geometric group theory, as well as algebra and combinatorics. The assumed background is basic group theory, including group actions, and basic algebraic topology, together with some knowledge of Riemannian geometry.

Author : Zhen-Qing Chen,Masatoshi Fukushima
Publisher : Princeton University Press
Page : 496 pages
File Size : 55,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691136059

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Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) by Zhen-Qing Chen,Masatoshi Fukushima Pdf

This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes. This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.

Author : Glyn Harman
Publisher : Princeton University Press
Page : 378 pages
File Size : 54,6 Mb
Release : 2020-05-26
Category : Mathematics
ISBN : 9780691202990

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Prime-Detecting Sieves (LMS-33) by Glyn Harman Pdf

This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre's form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec. Prime-Detecting Sieves breaks new ground by bringing together several different types of problems that have been tackled with modern sieve methods and by discussing the ideas common to each, in particular the use of Type I and Type II information. No other book has undertaken such a systematic treatment of prime-detecting sieves. Among the many topics Glyn Harman covers are primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander and Iwaniec on primes that are a sum of a square and a fourth power, and Heath-Brown's work on primes represented as a cube plus twice a cube. This book contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers.

Author : C. S. Aravinda,F. T. Farrell,J.-F. Lafont
Publisher : Cambridge University Press
Page : 378 pages
File Size : 45,8 Mb
Release : 2016-01-21
Category : Mathematics
ISBN : 9781107529007

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Geometry, Topology, and Dynamics in Negative Curvature by C. S. Aravinda,F. T. Farrell,J.-F. Lafont Pdf

Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.

Author : Anonim
Publisher : Unknown
Page : 506 pages
File Size : 51,5 Mb
Release : 2004
Category : Geometry
ISBN : UOM:39015060984153

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Geometry & Topology by Anonim Pdf

Author : Thomas Wolfgang Müller
Publisher : Cambridge University Press
Page : 608 pages
File Size : 50,7 Mb
Release : 2004-04-08
Category : Mathematics
ISBN : 0521542871

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Groups by Thomas Wolfgang Müller Pdf

Survey and research articles from the Bielefeld conference on topological, combinatorial and arithmetic aspects of groups.

Author : Jean-Marie Morvan,Leopold Verstraelen
Publisher : World Scientific
Page : 260 pages
File Size : 49,6 Mb
Release : 1989-04-01
Category : Electronic
ISBN : 9789814656726

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Geometry and Topology of Submanifolds by Jean-Marie Morvan,Leopold Verstraelen Pdf

Contents:Morse Theory of Minimal Two-Spheres and Curvature of Riemannian Manifolds (J D Moore)Isoparametric Systems (A West)The Gauss Map of Flat Tori in S3 (J L Weiner)On Totally Real Surfaces in Sasakian Space Forms (B Opozda)The Riemannian Geometry of Minimal Immersions of S2 into CPn (J Bolton & L M Woodward)Totally Real Submanifolds (F Urbano)Notes on Totally Umbilical Submanifolds (R Deszcz)Totally Complex Submanifolds of Quaternionic Projective Space (A Martínez)Symmetries of Compact Symmetric Spaces (B Y Chen)Nonnegatively Curved Hypersurfaces in Hyperbolic Space (S B Alexander & R J Currier)Semi-Parallel Immersions (J Deprez)Parallel Hypersurfaces (S A Robertson)Surfaces in Spheres and Submanifolds of the Nearly Kaehler 6–Sphere (F Dillen & L Vrancken)Semi-Symmetric Hypersurfaces (I van de Woestijne)Canonical Affine Connection on Complex Hypersurfaces of the Complex Affine Space (F Dillen & L Vrancken)and other papers Readership: Mathematicians.

Author : Martin R. Bridson,André Häfliger
Publisher : Springer Science & Business Media
Page : 665 pages
File Size : 50,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662124949

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Metric Spaces of Non-Positive Curvature by Martin R. Bridson,André Häfliger Pdf

A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.

Author : Mladen Bestvina,Michah Sageev,Karen Vogtmann
Publisher : American Mathematical Soc.
Page : 417 pages
File Size : 50,7 Mb
Release : 2014-12-24
Category : Mathematics
ISBN : 9781470412272

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Geometric Group Theory by Mladen Bestvina,Michah Sageev,Karen Vogtmann Pdf

Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Author : Ken’ichi Ohshika,Athanase Papadopoulos
Publisher : Springer Nature
Page : 525 pages
File Size : 47,5 Mb
Release : 2022-08-02
Category : Mathematics
ISBN : 9783030975609

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In the Tradition of Thurston II by Ken’ichi Ohshika,Athanase Papadopoulos Pdf

The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.

Author : Benson Farb
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 40,9 Mb
Release : 2006-09-12
Category : Class groups (Mathematics)
ISBN : 9780821838389

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Problems on Mapping Class Groups and Related Topics by Benson Farb Pdf

The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.

Author : Kenneth Stephenson
Publisher : Cambridge University Press
Page : 380 pages
File Size : 43,8 Mb
Release : 2005-04-18
Category : Mathematics
ISBN : 0521823560

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Introduction to Circle Packing by Kenneth Stephenson Pdf

Publisher Description

Author : Tomotada Ohtsuki
Publisher : Unknown
Page : 600 pages
File Size : 42,6 Mb
Release : 2002
Category : Knot theory
ISBN : UVA:X004843963

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Invariants of Knots and 3-manifolds (Kyoto 2001) by Tomotada Ohtsuki Pdf